Question

How do you simplify `\sqrt { 40m ^ { 4} n ^ { 3} }`?

Answer 1

$$2\sqrt{10}m^2\sqrt{n^3}$$

Explanation:

$$\sqrt{40m^4n^3}$$

$$\sqrt{40}\sqrt{m^4}\sqrt{n^3}$$
In the next step, we assume that $$m^2$$ is positive (i.e. m is real):
$$\sqrt{40}m^2\sqrt{n^3}$$
$$\sqrt{4\times 10}m^2\sqrt{n^3}$$
$$\sqrt{4}\sqrt{10}m^2\sqrt{n^3}$$
$$2\sqrt{10}m^2\sqrt{n^3}$$